Show the Proof¶

In [1]:

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

Out[1]:

	step type	requirements	statement
0	instantiation	1, 2, 3	, , , , , , , , , ⊢
	: , :
1	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_right_closure
2	assumption		⊢
3	instantiation	4, 5	, , , , , , , , ⊢
	:
4	theorem		⊢
	proveit.physics.quantum.algebra.qmult_nested_closure
5	instantiation	40, 6, 7	, , , , , , , , ⊢
	: , : , :
6	instantiation	8, 9, 10	, , , , , , , , ⊢
	: , :
7	instantiation	47, 11, 12	⊢
	: , : , :
8	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_left_closure
9	instantiation	40, 13, 14	, , , , , , , , ⊢
	: , : , :
10	instantiation	15, 62, 63	, ⊢
	: , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.posnat6
12	instantiation	16	⊢
	: , : , : , : , : , :
13	instantiation	17, 18, 57, 19	, , , , , , , , ⊢
	: , : , :
14	instantiation	47, 20, 21	⊢
	: , : , :
15	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
17	theorem		⊢
	proveit.physics.quantum.algebra.qmult_complex_ket_closure
18	instantiation	40, 22, 23	, , , , , , , ⊢
	: , : , :
19	assumption		⊢
20	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
21	instantiation	24	⊢
	: , : , : , : , :
22	instantiation	25, 44, 57, 26, 27	, , , , , , , ⊢
	: , : , : , :
23	instantiation	47, 28, 29	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
25	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
26	instantiation	50, 44, 57, 30	, , , , , , ⊢
	: , : , :
27	assumption		⊢
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
29	instantiation	31	⊢
	: , : , : , :
30	instantiation	40, 32, 33	, , , , , , ⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
32	instantiation	55, 34, 44, 57, 35	, , , , , , ⊢
	: , : , : , :
33	instantiation	47, 36, 37	⊢
	: , : , :
34	assumption		⊢
35	instantiation	50, 44, 57, 38	, , , , , ⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
37	instantiation	39	⊢
	: , : , :
38	instantiation	40, 41, 42	, , , , , ⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
40	theorem		⊢
	proveit.logic.equality.sub_left_side_into
41	instantiation	43, 44, 62, 57, 45, 46	, , , , , ⊢
	: , : , : , : , :
42	instantiation	47, 48, 49	⊢
	: , : , :
43	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
44	instantiation	67, 70	⊢
	:
45	instantiation	50, 62, 57, 51	, , ⊢
	: , : , :
46	instantiation	52, 69, 70, 53	, , , ⊢
	: , : , :
47	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
48	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
49	instantiation	54	⊢
	: , :
50	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
51	instantiation	55, 56, 62, 57, 58	, , ⊢
	: , : , : , :
52	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
53	modus ponens	59, 60	, , , ⊢
54	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
55	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
56	assumption		⊢
57	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
58	instantiation	61, 62, 63	, ⊢
	: , :
59	instantiation	64, 75, 65, 66	, , ⊢
	: , : , : , : , : , :
60	assumption		⊢
61	theorem		⊢
	proveit.physics.quantum.algebra.qmult_bra_is_linmap
62	instantiation	67, 69	⊢
	:
63	assumption		⊢
64	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
65	instantiation	68, 69, 70	, ⊢
	: , :
66	instantiation	71, 72	⊢
	: , :
67	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
68	theorem		⊢
	proveit.linear_algebra.matrices.complex_matrix_space_is_vec_space
69	assumption		⊢
70	assumption		⊢
71	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
72	instantiation	73, 74, 75	⊢
	: , : , :
73	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
75	assumption		⊢